Lesson 3
Modeling Real World Problems

 Name:etp Section:M2 Start Time:9:31:35 Instructor:pate Course:355

1) Please explain or describe when you think numerical modeling might be useful and/or necessary. For what kinds of problems or situations is it useful? Give at least three specific examples of scenarios or problems for which it is useful.

2) To use the Euler Method to numerically find position, velocity, and acceleration as a function of time, we will use the following set of basic general equations:

an = F(xn-1, vn-1, tn-1)/mn-1
vn = vn-1 + an-1*Dt
xn = xn-1 + vn-1*Dt
tn = tn-1 + Dt

Note: We'll be implementing this in Mathcad. In a given equation, Mathcad can't refer back to a number or variable in the same step (n value), so vn refers back to vn-1 and an-1.

Given all this and what's in your reading handout, write down what you think the Mathcad equations would be for modeling the motion of a 2d projectile where a drag force Fdrag = kv is acting. The key thing here is to use the general expression a = F/m to get a specific expression for the acceleration for this particular problem. (To make the typing simpler, use a notation like "x_n-1" for "xn-1" and "vx_n" for the x component of vn, etc.)

3) Suppose you jump out of a "perfectly good airplane" and experience 1d freefall with drag on your way down. If the drag force can be modeled as Fdrag = D*v2 where v is your speed and D is a constant, and your terminal speed is about 3 m/s with the chute open, which of the following is the best value for the coefficient D?

1. 0.6 kg/m
2. 6 kg/m
3. 60 kg/m
4. 600 kg/m

Below is a space for your thoughts, including general comments about today's assignment (what seemed impossible, what reading didn't make sense, what we should spend class time on, what was "cool", etc.):

You may change your mind as often as you wish. When you are satisfied with your responses click the SUBMIT button.

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